String scale in noncommutative Yang–Mills Original Research Article

We identify the effective string scale of noncommutative Yang–Mills theory (NCYM) with the noncommutativity scale through its dual supergravity description. We argue that Newtonʹs force law may be obtained with 4 dimensional NCYM with maximal SUSY. It provides a nonperturbative compactification mechanism of IIB matrix model. We can associate NCYM with the von Neumann lattice by the bi-local representation. We argue that it is superstring theory on the von Neumann lattice. We show that our identification of its effective string scale is consistent with exact T-duality (Morita equivalence) of NCYM.